Related papers: Uniqueness properties of functionals with Lipschit…

We provide comparison principles for convex functions through its proximal mappings. Consequently, we prove that the norm of the proximal operator determines a convex the function up to a constant. A new characterization of Lipschitzianity…

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…

In this paper we establish the existence of extremals for the Log Sobolev functional on complete non-compact manifolds with Ricci curvature bounded from below and strictly positive injectivity radius, under a condition near infinity. When…

We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `kernel' in which the points of differentiability of each…

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in…

In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…

We consider the joint value distribution of Dirichlet $L$-functions in the critical strip $\frac{1}{2} < \sigma < 1$. We show that the values of distinct Dirichlet $L$-functions are dependent in the sense that they do not behave like…

In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider $p-$Dirichlet type functionals on a suitable class of measure preserving maps $u: B\subset \mathbb{R}^2 \mapsto…

We obtain a probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space $[0,T]\times\mathbb{R}^d$, $d\ge 1$. To the best of our knowledge this is the only existing proof…

We prove the concavity of classical solutions to a wide class of degenerate elliptic differential equations on strictly convex domains of the unit sphere. The proof employs a suitable two-point maximum principle, a technique which…

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…

Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.

We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the…

In this paper we investigate the nature of stationary points of functionals on the space of Riemannian metrics on a smooth compact manifold. Special cases are spectral invariants associated with Laplace or Dirac operators such as functional…

We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, are strongly…

Let $n\geq 1$, $K>0$, and let $X=(X_1,X_2,\dots,X_n)$ be a random vector in $\mathbb{R}^n$ with independent $K$--subgaussian components. We show that for every $1$--Lipschitz convex function $f$ in $\mathbb{R}^n$ (the Lipschitzness with…

For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a…

Given a length function on the set of edges of a finite graph, the corresponding Fujiwara Laplacian is defined. We consider a problem of maximizing the first nonzero eigenvalue of this graph Laplacian over all choices of edge-length…

A characterization of dynamically defined zeta functions is presented. It comprises a list of axioms, natural extension of the one which characterizes topological degree, and a uniqueness theorem. Lefschetz zeta function is the main (and…

For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations.…